Deck 22: The Electric Field Ii: Continuous Charge Distributions

Question 1

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m².The electric field on the axis of the disk at a distance of 0.10 cm is approximately

A)0.34 MN/C
B)68 kN/C
C)99 kN/C
D)0.54 MN/C
E)18 kN/C

Answer 1

0.34 MN/C

Question 2

Consider a uniform electric field = (5.0 kN/C) .What is the flux of this field through a square of side 20 cm in a plane parallel to the yz plane?

A)0.10 kN · m²/C
B)0.20 kN · m²/C
C)0.40 kN · m²/C
D)0.50 kN · m²/C
E)0.13 kN · m²/C

Answer 2

0.20 kN · m²/C

Question 3

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0.A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm.What is the flux through the curved surface of the cylinder?

A)zero
B)1.3 kN · m²/C
C)0.25 kN · m²/C
D)1.3 N · m²/C
E)0.13 MN · m²/C

Answer 3

zero

Question 4

A uniform line charge of linear charge density $\lambda$ = 10.0 nC/m extends from x = 5 m to x = 8 m.The magnitude of the electric field at x = 10 m is

A)27.0 N/C
B)9.62 N/C
C)15.3 N/C
D)18.8 N/C
E)37.5 N/C

Question 5

An infinite plane lies in the yz-plane and it has a uniform surface charge density.The electric field at a distance x from the plane

A)decreases linearly with x.
B)decreases as 1/x².
C)is constant and does not depend on x.
D)increases linearly with x.
E)is undetermined.

Question 6

Consider a uniform electric field = (5.0 kN/C) .What is the flux of this field through a square of side 20 cm if the normal to its plane makes a 45º angle with the x axis?

A)71 N · m²/C
B)0.14 kN · m²/C
C)0.28 kN · m²/C
D)0.35 kN · m²/C
E)0.19 kN · m²/C

Question 7

Use the following figure to answer the problem:

-An infinite line charge of linear density $\lambda$ = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The x component of the electric field at the point P on the x axis at x = 3.0 m is approximately

A)1.8 kN/C
B)4.2 kN/C
C)0.96 kN/C
D)5.2 kN/c
E)0.64 mN/C

Question 8

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0.A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm.What is the flux through each end of the cylinder?

A)zero
B)1.3 kN · m²/C
C)0.25 kN · m²/C
D)13 N · m²/C
E)0.13 MN · m²/C

Question 9

Which of the following circumstances about Gauss's law is true?

A)Gauss's law is applicable in highly symmetric cases such as uniformly charged infinite plane,infinite cylinder,or sphere.
B)Gauss's law is applicable for a point charge.
C)Gauss's law is applicable for two or more point charges.
D)Gauss's law is applicable for any objects of any shape.
E)all of the above

Question 10

A uniform circular ring has charge Q and radius r.The magnitude of the electric field at a distance of r along the axis of the ring is E_o.If the radius were to double,then calculate the new electric field at a distance of r along the axis of the ring in terms of E_o.

A)0.40 E_o
B)0.25 E_o
C)0.50 E_o
D)0.20 E_o
E)0.089 E_o

Question 11

Use the following figure to answer the problem:

-An infinite line charge of linear density $\lambda$ = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The electric field at the point P on the x axis at x = 3.0 m is approximately

A)(4.2 kN/C)
B)(4.2 kN/C) + (0.64 kN/C)
C)(-0.96 kN/C)
D)(2.8 kN/C) + (0.64 kN/C)
E)(5.2 kN/C) - (2.3 kN/C)

Question 12

Use the following figure to answer the problem:

-An infinite line charge of linear density $\lambda$ = 0.30 µC/m lies along the z axis and a point charge q = 6.0 µC lies on the y axis at y = 2.0 m.The y component of the electric field at the point P on the x axis at x = 3.0 m is approximately

A)1.8 kN/C
B)2.3 kN/C
C)0.96 kN/C
D)4.2 kN/C
E)2.8 kN/C

Question 13

A uniform circular ring has charge Q = 7.36 $\mu$ C,and radius r = 3.33 cm.Calculate the magnitude of the electric field at a distance of 4.20 cm along the axis of the ring.

A)1.81 $\times$ 10¹ N/C
B)6.52 N/C
C)1.44 $\times$ 10⁷ N/C
D)1.44 $\times$ 10¹ N/C
E)1.81 $\times$ 10⁷ N/C

Question 14

A conducting circular disk has a uniform positive surface charge density.Which of the following diagrams best represents the electric field lines from the disk? (The disk is drawn as a cross-section.)

A)1
B)2
C)3
D)4
E)none of the diagrams

Question 15

A uniform line charge of linear charge density $\lambda$ = 5.00 nC/m extends from x = 0 to x = 10 m.The magnitude of the electric field at the point y = 12 m on the perpendicular bisector of the finite line of charge is

A)18.8 N/C
B)15.3 N/C
C)9.65 N/C
D)4.27 N/C
E)2.88 N/C

Question 16

A uniform line charge of linear charge density $\lambda$ = 10.0 nC/m extends from x = 5 m to x = 8 m.The magnitude of the electric field at the point y = 5 m on the perpendicular bisector of the finite line of charge is

A)3.86 N/C
B)5.79 N/C
C)8.31 N/C
D)10.3 N/C
E)12.6 N/C

Question 17

A uniform circular ring has charge Q and radius r.A uniformly charged disk also has charge Q and radius r.Calculate the electric field at a distance of r along the axis of the ring divided by the electric field at a distance of r along the axis of the disk.

A)1.0
B)0.60
C)1.7
D)0.50
E)0.85

Question 18

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m².The electric field on the axis of the disk at a distance of 5.0 m is approximately

A)0.34 MN/C
B)68 kN/C
C)99 kN/C
D)0.54 MN/C
E)18 kN/C

Question 19

A disk of radius 10 cm carries a uniform surface charge density of 6.0 µC/m².The electric field on the axis of the disk at a distance of 10 cm is approximately

A)0.34 MN/C
B)68 kN/C
C)99 kN/C
D)0.54 MN/C
E)18 kN/C

Question 20

A uniform line charge of linear charge density $\lambda$ = 5.00 nC/m extends from x = 0 to x = 10 m.The magnitude of the electric field at x = 12 m is

A)3.86 N/C
B)9.62 N/C
C)15.3 N/C
D)18.8 N/C
E)37.5 N/C

Question 21

Use the following figure to answer the next problem:

-A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³.What is the electric field at r = 3.0 cm?

A)36.0 N/C
B)230 N/C
C)140 N/C
D)565 N/C
E)450 N/C

Question 22

Use the following figure to answer the next problem:

-A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³.What is the electric field at r = 8.1 cm?

A)0.12 kN/C
B)1.5 kN/C
C)0.74 kN/C
D)2.3 kN/C
E)12 kN/C

Question 23

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density $\rho$ = 200 nC/m³.What is the electric field at r = 8.0 cm?

A)0.23 kN/C
B)0.11 kN/C
C)57 N/C
D)0.44 kN/C
E)zero

Question 24

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density $\rho$ = 200 nC/m³.What is the electric field at r = 2.0 cm?

A)zero
B)0.11 kN/C
C)57 N/C
D)0.44 kN/C
E)0.23 kN/C

Question 25

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 2.0 cm is approximately

A)12 kN/C
B)0.56 kN/C
C)1.3 kN/C
D)0.81 kN/C
E)zero

Question 26

Use the following figure to answer the next problem:

-A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where r < a,is which of the following,in terms of k = (4 $\pi\varepsilon$ ₀)^-1?

A)kQ/r²
B)kQr/a³
C)kQ/a²
D)kQ/b²
E)zero

Question 27

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density $\rho$ = 200 nC/m³.What is the electric field at r = 3.9 cm?

A)zero
B)0.44 kN/C
C)57 N/C
D)0.11 kN/C
E)0.23 kN/C

Question 28

Use the following figure to answer the next problem:

-A hollow metal sphere has a total charge of 100 µC.If the radius of the sphere is 50 cm,the electric field intensity at a distance of 3.0 m from the surface of the sphere is approximately

A)3.0 $\times$ 10⁵ N/C
B)2.6 $\times$ 10⁵ N/C
C)1.0 $\times$ 10⁵ N/C
D)7.4 $\times$ 10⁴ N/C
E)3.6 $\times$ 10⁶ N/C

Question 29

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0.A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm.What is the net charge inside the cylinder?

A)zero
B)22 nC
C)0.22 nC
D)4.5 nC
E)2.2 µC

Question 30

A surface is so constructed that,at all points on the surface,the vector points outward.Therefore,it can be said that

A)the surface encloses a net positive charge.
B)the surface encloses a net negative charge.
C)the surface encloses no net charge.
D)the surface vector $\Delta$ S at all points on the surface is necessarily parallel to the electric field vector .
E)the surface vector $\Delta$ S at all points on the surface is necessarily perpendicular to the electric field vector .

Question 31

Use the following figure to answer the next problem:

-A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where a < r < b,is which of the following,in terms of k = (4 $\pi\varepsilon$ ₀)^-1?

A)kQ/r²
B)2kQ/r²
C)kQ/a²
D)kQ/b²
E)kQ/(b - a)²

Question 32

Use the following figure to answer the next problem:

-A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³.What is the electric field at r = 20 cm?

A)0.24 kN/C
B)0.12 kN/C
C)4.8 N/C
D)15 N/C
E)5.4 N/C

Question 33

Use the following figure to answer the next problem:

-A solid sphere of radius a is concentric with a hollow sphere of radius b,where b > a.If the solid sphere has a charge +Q and the hollow sphere a charge of -Q,the electric field at radius r,where r > b,is which of the following,in terms of k = (4 $\pi\varepsilon$ ₀)^-1?

A)kQ/r²
B)2kQ/r²
C)kQ/a²
D)kQ/b²
E)zero

Question 34

An infinitely long cylinder of radius 4.0 cm carries a uniform volume charge density $\rho$ = 200 nC/m³.What is the electric field at r = 4.1 cm?

A)zero
B)0.11 kN/C
C)57 N/C
D)0.44 kN/C
E)0.23 kN/C

Question 35

A cube of side 3.56 cm has a charge of 9.11 $\mu$ C placed at its center.Calculate the electric flux through one side of the cube.

A)1.03 $\times$ 10⁶ N^.m²/C
B)2.58 $\times$ 10⁵ N^.m²/C
C)8.13 $\times$ 10⁸ N^.m²/C
D)1.72 $\times$ 10⁵ N^.m²/C
E)1.35 $\times$ 10⁸ N^.m²/C

Question 36

An electric field is = (400 N/C) for x > 0 and = (-400 N/C) for x < 0.A cylinder of length 30 cm and radius 10 cm has its center at the origin and its axis along the x axis such that one end is at x = +15 cm and the other is at x = -15 cm.What is the net outward flux through the entire cylindrical surface?

A)zero
B)2.5 kN · m²/C
C)0.50 kN · m²/C
D)25 N · m²/C
E)0.25 MN · m²/C

Question 37

A surface is so constructed that,at all points on the surface,the vector points inward.Therefore,it can be said that

A)the surface encloses a net positive charge.
B)the surface encloses a net negative charge.
C)the surface encloses no net charge.
D)the surface vector $\Delta$ S at all points on the surface is necessarily parallel to the electric field vector .
E)the surface vector $\Delta$ S at all points on the surface is necessarily perpendicular to the electric field vector .

Question 38

A hollow spherical shell of radius 5.36 cm has a charge of 1.91 $\mu$ C placed at its center.Calculate the electric flux through an area of 1.20 $\times$ 10^-2 m² on the shell.

A)6.48 $\times$ 10⁵ N^.m²/C
B)2.16 $\times$ 10⁵ N^.m²/C
C)7.20 $\times$ 10⁴ N^.m²/C
D)2.16 $\times$ 10¹ N^.m²/C
E)none of the above

Question 39

Use the following figure to answer the next problem:

-A sphere of radius 8.0 cm carries a uniform volume charge density $\rho$ = 500 nC/m³.What is the electric field at r = 7.9 cm?

A)16 N/C
B)3.3 N/C
C)60 N/C
D)9.5 N/C
E)1.5 kN/C

Question 40

A horizontal surface of area 0.321 m² has an electric flux of 123 N^.m²/C passing through it at an angle of 25° to the horizontal.If the flux is due to a uniform electric field,calculate the magnitude of the latter.

A)907 N^.m²/C
B)423 N^.m²/C
C)1.10 $\times$ 10^-3 N^.m²/C
D)2.36 $\times$ 10^-3 N^.m²/C
E)383 N^.m²/C

Question 41

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 5.9 cm is approximately

A)0.81 kN/C
B)zero
C)1.3 kN/C
D)12 kN/C
E)0.56 kN/C

Question 42

The electric field for a spherical shell of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A) $\varepsilon$ ₀/ $\sigma$
B) $\sigma$ / $\varepsilon$ ₀
C) $\varepsilon$ ₀/ $\sigma$ ²
D) $\varepsilon$ ₀2/ $\sigma$ ²
E) $\sigma$ ²/ $\varepsilon$ ₀

Question 43

For a uniformly charged spherical sphere of radius R carrying a total charge Q,calculate the electric field at a distance R/2 outside the sphere divided by the electric field at a distance R/2 inside the sphere.

A)9/8
B)infinity
C)4/9
D)8.0
E)8/9

Question 44

Electrical conductors contain

A)only free electrons.
B)only bound electrons.
C)both free and bound electrons.
D)neither bound nor free electrons.
E)only protons and neutrons.

Question 45

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density
The electric at y = b where 0 < b < d is

A)
B)
C)
D)
E)

Question 46

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 30 cm.

A)5.2 $\times$ 10⁹ N/C
B)2.6 $\times$ 10¹¹ N/C
C)8.2 $\times$ 10¹⁰ N/C
D)4.7 $\times$ 10¹¹ N/C
E)4.9 $\times$ 10¹⁰ N/C

Question 47

A large,flat conducting plate has a surface charge density $\sigma$ = 8.0 $\times$ 10^-9 C/m² on one of its surfaces.What is the magnitude of the electric field 10 µm from this plate?

A)72 N/C
B)0.23 kN/C
C)0.90 kN/C
D)90 MN/C
E)9.0 $\times$ 10¹² N/C

Question 48

A solid spherical conductor has a radius of 15 cm.The electric field 30 cm from the center of this sphere has a magnitude of 800 N/C.What is the surface charge density $\sigma$ on the sphere?

A)7.1 $\times$ 10^-9 C/m²
B)1.0 $\times$ 10^-8 C/m²
C)1.4 $\times$ 10^-8 C/m²
D)2.8 $\times$ 10^-8 C/m²
E)1.1 $\times$ 10^-7 C/m²

Question 49

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 6.1 cm is approximately

A)0.81 kN/C
B)zero
C)1.3 kN/C
D)12 kN/C
E)0.56 kN/C

Question 50

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 16 cm is approximately

A)0.32 kN/C
B)1.0 kN/C
C)zero
D)0.13 kN/C
E)0.53 kN/C

Question 51

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 9.1 cm is approximately

A)zero
B)1.0 kN/C
C)0.65 kN/C
D)0.32 kN/C
E)0.13 kN/C

Question 52

A non-conducting pipe has a uniform charge density of 50 C/m³.The inner radius of the pipe is 25 cm,while the outer radius is 35 cm.Calculate the magnitude of the electric field at r = 40 cm.

A)6.8 $\times$ 10¹¹ N/C
B)8.5 $\times$ 10¹¹ N/C
C)4.2 $\times$ 10¹¹ N/C
D)1.3 $\times$ 10¹¹ N/C
E)8.7 $\times$ 10¹⁰ N/C

Question 53

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 8.9 cm is approximately

A)1.0 kN/C
B)0.13 kN/C
C)0.32 kN/C
D)zero
E)0.65 kN/C

Question 54

An infinitely long cylindrical shell of radius 6.0 cm carries a uniform surface charge density $\sigma$ = 12 nC/m².The electric field at r = 10 cm is approximately

A)12 kN/C
B)0.56 kN/C
C)1.3 kN/C
D)0.81 kN/C
E)zero

Question 55

The electric field at the surface of a conductor

A)is parallel to the surface.
B)depends only on the total charge on the conductor.
C)depends only on the area of the conductor.
D)depends only on the curvature of the surface.
E)depends on the area and curvature of the conductor and on its charge.

Question 56

Which diagram best represents the electric field along the y-axis?

A)1
B)2
C)3
D)4
E)none of the diagrams

Question 57

The electric field for an infinite plane of charge is discontinuous by the amount _____ at a point where there is a surface charge density $\sigma$ .

A) $\varepsilon$ ₀/ $\sigma$
B) $\sigma$ / $\varepsilon$ ₀
C) $\varepsilon$ ₀/ $\sigma$ ²
D) $\varepsilon$ ₀2/ $\sigma$ ²
E) $\sigma$ ²/ $\varepsilon$ ₀

Question 58

A spherical shell of radius 9.0 cm carries a uniform surface charge density $\sigma$ = 9.0 nC/m².The electric field at r = 4.0 cm is approximately

A)0.13 kN/C
B)1.0 kN/C
C)0.32 kN/C
D)0.75 kN/C
E)zero

Question 59

Use the figure for the next problem. An infinite slab of thickness 2d lies in the xz–plane. The slab has a uniform volume charge density
The electric at y = b where b > d is

A)
B)
C)
D)
E)

Question 60

For a solid uniformly charged sphere of radius R,calculate the electric field at a distance R/2 outside the sphere,divided by the electric field at a distance R/2 inside the sphere.

A)9/8
B)infinity
C)2.0
D)8.0
E)8/9

Question 61

The surface charge density for r = r_b1 is

A)Q/( $\pi$ r_b1²)
B)- Q/( $\pi$ r_b1²)
C)Q/(4 $\pi$ r_b1²)
D)- Q/(4 $\pi$ r_b1²)
E)zero

Question 62

Use the following scenario for the next question. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r_b1 < r < r_b2 is

A)-kQ/r²
B)kQ/r²
C)-2kQ/r
D)2kQ/r
E)zero

Question 63

Use the following scenario for the next question. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r > r_b1 is

A)-kQ/r²
B)kQ/r²
C)-2kQ/r
D)2kQ/r
E)zero

Question 64

Use the following scenario for the next question. A solid conducting sphere of radius ra is placed concentrically inside a conducting spherical shell of inner radius r_b1 and outer radius r_b2. The inner sphere carries a charge Q while the outer sphere does not carry any net charge.

-The electric field for r_a < r < r_b1 is

A)-kQ/r²
B)kQ/r²
C)-2kQ/r
D)2kQ/r
E)zero